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Expenses and Other Non-Operating Income/(Expense), Net - Schedule Of Sales And Marketing Expenses (Details) - USD ($)	6 Months Ended
	Jun. 30, 2025	Jun. 30, 2024
Expenses And Other Non Operating Income Expense Net [Abstract]
Total	$ 3,619,675	$ 1,662,048

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- References

No definition available.

+ Details

Name:	rzlv_ExpensesAndOtherNonOperatingIncomeExpenseNetAbstract
Namespace Prefix:	rzlv_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

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- Definition

The aggregate total amount of expenses directly related to the marketing or selling of products or services.

+ References

No definition available.

+ Details

Name:	us-gaap_SellingAndMarketingExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration